125 research outputs found
Moduli of -algebras
We describe a homotopy-theoretic approach to the moduli of -algebras of
Blanc-Dwyer-Goerss using the -category of
product-preserving presheaves on finite-wedges of positive-dimensional spheres,
reproving all of their results in this new setting
Derived -Geometry I: Foundations
This work is the first in a series laying the foundations of derived geometry
in the setting, and providing tools for the construction and study
of moduli spaces of solutions of Partial Differential Equations that arise in
differential geometry and mathematical physics. To advertise the advantages of
such a theory, we start with a detailed introduction to derived
-geometry in the context of symplectic topology and compare and
contrast with Kuranishi space theory. In the body of this work, we avail
ourselves of Lurie's extensive work on abstract structured spaces to define
-categories of derived -ring and -schemes and
derived -rings and -schemes with corners via a
universal property in a suitable -category of -categories
with respect to the ordinary categories of manifolds and manifolds with corners
(with morphisms the -maps of Melrose in the latter case), and prove many
basic structural features about them. Along the way, we establish some derived
flatness results for derived -rings of independent interest.Comment: 203 pages; comments welcom
Toward a theory of the integer quantum Hall transition: continuum limit of the Chalker-Coddington model
An N-channel generalization of the network model of Chalker and Coddington is
considered. The model for N = 1 is known to describe the critical behavior at
the plateau transition in systems exhibiting the integer quantum Hall effect.
Using a recently discovered equality of integrals, the network model is
transformed into a lattice field theory defined over Efetov's sigma model space
with unitary symmetry. The transformation is exact for all N, no saddle-point
approximation is made, and no massive modes have to be eliminated. The naive
continuum limit of the lattice theory is shown to be a supersymmetric version
of Pruisken's nonlinear sigma model with couplings sigma_xx = sigma_xy = N/2 at
the symmetric point. It follows that the model for N = 2, which describes a
spin degenerate Landau level and the random flux problem, is noncritical. On
the basis of symmetry considerations and inspection of the Hamiltonian limit, a
modified network model is formulated, which still lies in the quantum Hall
universality class. The prospects for deformation to a Yang-Baxter integrable
vertex model are briefly discussed.Comment: 25 pages, REVTEX, calculation of sigma_xx correcte
Higher Topos Theory
This purpose of this book is twofold: to provide a general introduction to
higher category theory (using the formalism of "quasicategories" or "weak Kan
complexes"), and to apply this theory to the study of higher versions of
Grothendieck topoi. A few applications to classical topology are included.Comment: 735 pages. An updated and expanded version of the earlier submission
math.CT/0306109 2/10/07: Various minor additions and corrections; added some
material on combinatorial model categories to the appendix. 3/8/7: Actually
uploaded the update this time; added material on fiber products of higher
topoi. 7/31/08: Several sections added, others rewritte
(1,0) superconformal models in six dimensions
We construct six-dimensional (1,0) superconformal models with non-abelian
gauge couplings for multiple tensor multiplets. A crucial ingredient in the
construction is the introduction of three-form gauge potentials which
communicate degrees of freedom between the tensor multiplets and the Yang-Mills
multiplet, but do not introduce additional degrees of freedom. Generically
these models provide only equations of motions. For a subclass also a
Lagrangian formulation exists, however it appears to exhibit indefinite metrics
in the kinetic sector. We discuss several examples and analyze the excitation
spectra in their supersymmetric vacua. In general, the models are
perturbatively defined only in the spontaneously broken phase with the vev of
the tensor multiplet scalars serving as the inverse coupling constants of the
Yang-Mills multiplet. We briefly discuss the inclusion of hypermultiplets which
complete the field content to that of superconformal (2,0) theories.Comment: 30 pages, v2: Note, some comments and references adde
- …